Finite element analysis (FEA) is a computer aided engineering tool that uses numerical methods to obtain approximate solutions to complex engineering systems. FEA is routinely used in many other engineering fields, especially structural designs. It is also widely used in simulating time-elapsed events, such as car crashing and metal forming. It is a very powerful tool and used extensively by engineers and scientists in evaluating new product designs and existing product refinements prior to actual manufacturing and construction. FEA is generally implemented as finite element analysis software or application module to be installed in a computer system.
To perform a FEA, a finite element analysis model is first created based on the geometry of the structure under analysis. In the model, the subject structure is reduced to a finite number of nodes, which are inter-connected to by elements or finite elements. Material properties are assigned to the elements. The number of the nodes and the type of elements can be chosen to fit the specific needs and interests for the system in a finite element analysis. Additionally, constraints are placed on the model to ensure proper boundary conditions.
There are many types of finite elements: (1) one-dimensional element (e.g., beam element, truss element), (2) two-dimensional element (e.g., shell element), and (3) three-dimensional element (e.g., tetrahedral element, hexahedral element). Each finite element is implemented using a shape function to represent or describe its domain. The shape function may be low order (linear) or higher order (curve-linear). Elements that use low order shape function may require only corner nodes or end nodes, for example, an 8-node brick element 110A shown in FIG. 1A and a 4-node tetrahedral element 110B shown in FIG. 1B.
In order to use higher order shape function, elements require additional nodes, for example, a 20-node hexahedral element 110C shown in FIG. 1C and a 10-node tetrahedral element 110D shown in FIG. 1D. As a result of the additional nodes, computation becomes more complex thereby requiring more computing resources. This is a problem in today's production engineering environment as many of the modern FEA model comprises more than one million elements. In order to keep a reasonable turnaround time (e.g., overnight) for each FEA, users generally would like to use low order elements to maintain a reasonable turnaround time but still want to have the quality of the FEA results to include effects from high order shape function. It is noted that each node of the above mentioned prior art solid elements (i.e., elements 110A-B) include only translational deformation at each node, which is represented by three components u, v and w (i.e., three translational degrees-of-freedom) shown in respective Cartesian coordinate systems 100A-D.
Another problem arises when the prior art solid elements are used in conjunction with shell elements in one FEA model. Each node of the shell element has six degrees-of-freedom (DOFs) (i.e., three translational and three rotational), while the prior art solid element has only three translational DOFs. The incompatibility at common nodes shared between solid and shell elements often created numerical problem that rendered the simulation results useless. Therefore, it would be desirable to have an improved solid finite element that can overcome the problems and deficiencies in prior art approaches described above.